@Eli L
cPanel supports LetsEncrypt plugin - https://blog.cpanel.com/announcing-cpanel-whms-official-lets-encrypt-with-autossl-plugin/
Install Fast and Free SSL and HTTPS in cPanel with Let’s Encrypt explains the procedure to install autossl or other third party plugins

You can make backup of your account/database using cPanel. If its just database, you can also export database using phpMyAdmin. Eli may be able to help move to new plan with all existing files and database.

You can install Wordpress through cPanel > Software & Services > Site Software. Or you can install by following instructions at https://codex.wordpress.org/Installing_WordPress.
You can get linkback code from http://vlexofree.com/wiki/Ads_and_Linkbacks.
For editing the side bar, you can refer to https://codex.wordpress.org/Customizing_Your_Sidebar or https://wordpress.org/support/topic/where-to-edit-sidebar.